$\int x^{^{\frac12}}\,dx=$ $+C$
Answer: The integrand is of the form $x^n$ where $n\neq-1$, so we can use the reverse power rule: $\int x^n\,dx=\dfrac{x^{n+1}}{n+1}+C$ $\begin{aligned} \int x^{^{{\frac12}}}\,dx&=\dfrac{x^{^{{\frac12}+1}}}{{\dfrac12}+1}+C \\\\ &=\dfrac23x^{^{\frac32}}+C \end{aligned}$ In conclusion, $\int x^{^{\frac12}}\,dx=\dfrac23x^{^{\frac32}}+C$